What do you mean by "business" at Columbia? Also, my impression is that the work is pretty hard at Cornell, with much higher caps on admissions on call, for example. Columbia probably has a tougher intern year, but in my mind that's an asset. And the psychodynamic psychotherapy is pretty good at Columbia. Not all the residents at Columbia are interested in research, though there is a tendency for people to go into academic positions of some kind.
One of the heads of Columbia's psych department broke it to me this way (this was before my interview, we have known each other for over a year):
At Columbia, you will get superior research opportunities, but a lesser clinical exposure. One of the problems is that you just have less patient exposure at Columbia -- he said that you will get more at Cornell as well as NYU and Mount Sinai. (He said, you'll get 4x more of every type of psychopathology at NYU than at Columbia.)
As the previous poster said, Cornell does have superior psychodynamic training. It is a deep place -- very analytic -- and they are really focused on clinical training. Not just with the fourth year project, but the mentoring, etc.
Yes, for anyone who has ever been affiliated with Columbia, the administration can be maddening. That is the "business" at Columbia -- where you can get lost in the mix, where the whole institution is so disorganized.... Even my mentor in the Columbia psych department said, what we could really use is an MBA who can fix up the department as well as the whole hospital.
For research oriented people, those who want to do academic medicine that is 75% research and 25% clinical -- Columbia is perfect.
As far as the workload, I know multiple people in different years in both programs. Both work hard. Columbia's intern year, especially the medicine months, are near murderous -- eg. the notorious month of ICU ("rotation from Heck"). Maybe this makes you a better doctor, I don't know, but I think that most people would get more out of a month doing something else rather than ICU. Both work hard throughout, however.
And as for the housing, Columbia's is cheaper but is in Washington Heights (which few psych residents live in, since it is a dark, boring, and quite unpleasant place). Most residents live on the Upper West Side, where rents are typically very high for Manhattan -- I used to live in a so-so expensive area of the Upper West and my rent was $2900 for a 2BR. Cornell's housing -- there is nothing bad to say, it is relatively inexpensive and very nice.
Bottom line, both are up there with MGH, UCLA, whatever programs you want to consider to be the top tier -- all are fantastic. My advice is to pick what fits your personality and temperament, since that is the environment where you're most likely to thrive.